Element of the set

If mathematicians cannot reduce the concept of "set" to other concepts, then they do not understand anything in mathematics. I answer the question: how are the elements of one set different from the elements of another set? The answer is very simple: numbers and units of measurements.

Today everything belongs to some kind of set (as mathematicians assure us). By the way, did you look at yourself in the mirror? Have you seen on your forehead a list of those sets to which you belong? And I have not seen such a list. I will say more - not a single thing in reality has a tag with a list of sets to which this thing belongs. Sets are shamans' inventions. How do they do it? Let's recall the history and see how the elements of the set looked like before the mathematician-shamans pulled them into their sets.

Once upon a time, when no one had heard of mathematics, and only trees and Saturn had rings, huge herds of wild elements of sets roamed the physical fields (after all, shamans had not yet invented mathematical fields). They looked something like this.

Sea urhin

Yes, do not be surprised, from the point of view of mathematics, all the elements of sets are most similar to sea urchins - from one point, like needles, units of measurements stick out in all directions. For those who missed something, I remind you that any unit of measure can be represented geometrically as a segment of arbitrary length, and a number as a point. Geometrically, any value can be represented as a bunch of segments sticking out in different directions from one point. This point is point zero. I will not draw this work of geometric art (no inspiration), but you can easily imagine it.

What units of measurements form an element of the set? Any, describing this element from different points of view. These are the ancient units of measurement used by our ancestors and which everyone has long forgotten about. These are the modern units of measurement that we use now. These are units of measurement unknown to us that our descendants will come up with and which they will use to describe reality.

We figured out the geometry - the proposed model of the elements of the set has a clear geometric representation. What about physics? Units of measurement - this is the direct connection of mathematics with physics. If shamans do not recognize units of measurement as a full-fledged element of mathematical theories, this is their problem. Personally, I can’t imagine real math science without units of measurement. That is why, at the very beginning of the story about set theory, I spoke of it as a Stone Age.

But let us pass to the most interesting thing - to the algebra of elements of sets. Algebraically, any element of a set is a collection of different quantities. It looks like this.

Element of the set

I deliberately do not apply the conventions adopted in set theory, since we consider the element of the set in its natural environment before the advent of set theory. Each pair of letters designates a separate quantity consisting of a number indicated by the letter "n" and a unit of measurement indicated by the letter "a". Indexes indicate that the numbers and units are different. One element of the set can consist of an infinite number of quantities (how much imagination we have and our descendants). Each value is geometrically depicted as a separate segment. In the example with the sea urchin, one value is one needle.

How do shamans form sets of different elements? In fact, by units of measurement or by numbers. Without understanding anything in mathematics, they take different sea urchins and carefully examine them in search of the only needle by which they form a multitude. If there is such a needle, then this element belongs to the set, if there is no such needle, it is an element of another set. Shamans tell us tales about thought processes and a single whole.

As you may have guessed, one and the same element can belong to very different sets. Further I will show you how the sets, subsets and other attributes of shamans are formed.